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The $S U (3) \supset S O (3)$ $S U (3) \supset S O (3)$ missing label problem and the analytical Bethe Ansatz

Institut Denis-Poisson, CNRS/UMR 7013, Université de Tours, Parc de Grandmont, 37200 Tours, France

Institut Denis-Poisson, CNRS/UMR 7013, Université d’Orléans, Orléans Cedex 2, France

E-mail Address: crampe1977@gmail.com

Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-Ville Station, Montréal, Québec, H3C 3J7 Canada

E-mail Address: dounia.shaaban.kabakibo@umontreal.ca

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Luc Vinet

Insitut de Valorisation des données (IVADO), Montréal, Québec, H2S 3H1 Canada

E-mail Address: vinet@crm.umontreal.ca

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https://doi.org/10.1142/S0217751X22500385Cited by:2 (Source: Crossref)

Abstract

The missing label for basis vectors of $S U (3)$ $S U (3)$ representations corresponding to the reduction $S U (3) \supset S O (3)$ $S U (3) \supset S O (3)$ can be provided by the eigenvalues of $S O (3)$ $S O (3)$ scalars in the enveloping algebra of $s u (3)$ $s u (3)$ . There are only two such independent elements of degrees three and four. It is shown how the one of degree four can be diagonalized using the analytical Bethe ansatz.

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